Remark 7.5 In both cases, i.e. if \(b_{j,k} =|a_{j,k}|^{-\alpha }\)  or if \(b_{j,k} =\exp (-|a_{j,k}|)\) , we see that the series (REF ) diverges at the critical exponent \(t=\delta \) .
This in fact gives further information on the dimension \(\dim \mathcal {I}_R (f)\)  since it was observed in [1]} that one can then employ
[2]} in order to get
\(\text{{\rm HD}}(\mathcal {I}_R (f)) > \delta \) 
